Spin-orbit interaction in coupled quantum wells

We theoretically investigate the spin-orbit interaction in GaAs/AlxGa1 x As coupled quantum wells. We consider the contribution of the interface-related Rashba term as well as the linear and cubic Dresselhaus terms to the spin splitting. For the coupled quantum wells which bear an inherent structure inversion asymmetry, the same probability density distribution of electrons in the two step quantum wells results in a large spin splitting from the interface term. If the widths of the two step quantum wells are different, the electron probability density in the wider step quantum well is considerably higher than that in the narrower one, resulting in the decrease of the spin splitting from the interface term. The results also show that the spin splitting of the coupled quantum well is not significantly larger than that of a step quantum well.     

PbTe/PbSrTe半导体非对称量子阱中的Rashba效应

窄带隙半导体异质结构的自旋效应最近受到了国际上的很大关注.Ⅳ-Ⅵ族半导体具有各向异性和多能谷的特征,因此可以预期Rashba自旋效应在不同取向的Ⅳ-Ⅵ族半导体量子阱结构中存在显著差异.计算了多个取向的Pb_1-ySr_yTe/PbTe/Pb_1-xSr_xTe非对称量子阱中的Rashba分裂能,结果表明［100］取向的PbTe量子阱的Rashba分裂能在阱宽为5.0nm时 关键词： Ⅳ-Ⅵ族半导体 非对称量子阱 Rashba效应 自旋-轨道耦合分裂     

Rashba and Dresselhaus spin-orbit interaction in semiconductor quantum wells

We theoretically investigate the Rashba and Dresselhaus spin-orbit interaction in AlAs/GaAs/Al_0.3Ga_0.7As/AlAs step-quantum wells. The ratio of Rashba and Dresselhaus spin splitting can be effectively manipulated by the well width and step width in the absence of electric field and magnetic field. When the well width of the step-quantum well is wider than 10 nm, the total spin splitting, which contains the contribution of interface as well as linear and cubic Dresselhaus terms, is always the greatest when the width of GaAs layer equals to about 2 nm. When the well width is wider than 2 nm, two different step widths can meet the SU(2) symmetry conditions, the smaller one of them results in maximum spin relaxation time. We also predict the application of the step-quantum well in spintronic devices.     

Electronic structure of paramagnetic In<Subscript>1-x</Subscript>Mn<Subscript>x</Subscript> As nanowires

The electronic structure, spin splitting energies, and g factors of paramagnetic In_1-xMn_xAs nanowires under magnetic and electric fields are investigated theoretically including the sp-d exchange interaction between the carriers and the magnetic ion. We find that the effective g factor changes dramatically with the magnetic field. The spin splitting due to the sp-d exchange interaction counteracts the Zeeman spin splitting. The effective g factor can be tuned to zero by the external magnetic field. There is also spin splitting under an electric field due to the Rashba spin-orbit coupling which is a relativistic effect. The spin-degenerated bands split at nonzero k_z (k_z is the wave vector in the wire direction), and the spin-splitting bands cross at k_z = 0, whose k_z-positive part and negative part are symmetrical. A proper magnetic field makes the k_z-positive part and negative part of the bands asymmetrical, and the bands cross at nonzero k_z. In the absence of magnetic field, the electron Rashba coefficient increases almost linearly with the electric field, while the hole Rashba coefficient increases at first and then decreases as the electric field increases. The hole Rashba coefficient can be tuned to zero by the electric field.     

Influence of Polarization-Induced Electric Field on Subband Structure in AlxGa1-xN/GaN Double Quantum Wells

The influence of the polarization-induced electric field and other parameters on the subband structure in Al_xGa_1-xN /GaN coupled double quantum wells (DQWs) has been studied by solving the Schrödinger and Poisson equations self-consistently. It is found that the polarization effect leads to an asymmetric potential profile of Al_xGa_1-xN/GaN DQWs although the two wells have the same width and depth. The polarization effect also leads to a very large Stark shift between the odd and the even order subband levels that can reach 0.54eV. Due to the polarization-induced Stark shift, the wavelength of the intersubband transition between the first odd order and the second even order subband levels becomes smaller, which is useful for realization of optoelectronic devices operating within the telecommunication window region.     

Rashba spin splitting in the Al0.3Ga0.7N/GaN heterostructure under uniaxial strain

By solving the Schrödinger and Poisson equations self-consistently, changes of the Rashba spin splitting for the Al_0.3Ga_0.7N/GaN heterostructure under uniaxial strain are calculated, and electrons are found to take up the first two subbands. The additional polarization induced by the uniaxial strain leads to a great enhancement of the built-in electric field and the 2DEG concentration. The Rashba spin splitting almost increases linearly with the uniaxial strain, and its amplitude increases by 36% with a strain of 4×10⁻³. The effect of electrons occupying more than one subband on the Rashba spin splitting is discussed. Results show the internal electric field caused by the polarization is crucial for the considerable Rashba spin splitting in the Al_0.3Ga_0.7N/GaN heterostructure and the magnitude of the Rashba spin splitting can be greatly modulated by the uniaxial strain, which would benefit further research and application of spintronics.     

Zero field spin splitting in asymmetric quantum wells

Spin splitting of asymmetric quantum wells is theoretically investigated in the absence of any electric field, including the contribution of interface-related Rashba spin-orbit interaction as well as linear and cubic Dresselhaus spin-orbit interaction. The effect of interface asymmetry on three types of spin-orbit interaction is discussed. The results show that interface-related Rashba and linear Dresselhaus spin-orbit interaction can be increased and cubic Dresselhaus spin-orbit interaction can be decreased by well structure design. For wide quantum wells, the cubic Dresselhaus spin-orbit interaction dominates under certain conditions, resulting in decreased spin relaxation time.     

Spin Splitting in Different Semiconductor Quantum Wells

We theoretically investigate the spin splitting in four undoped asymmetric quantum wells in the absence of external electric field and magnetic field. The quantum well geometry dependence of spin splitting is studied with the Rashba and the Dresselhaus spin-orbit coupling included. The results show that the structure of quantum well plays an important role in spin splitting. The Rashba and the Dresselhaus spin splitting in four asymmetric quantum wells are quite different. The origin of the distinction is discussed in this work.     

Al0.6Ga0.4N/GaN/Al0.3Ga0.7N/Al0.6Ga0.4N量子阱中的Rashba自旋劈裂

正如人们所知, 可以通过电场或者设计非对称的半导体异质结构来调控体系的结构反演不对称性(SIA)和Rashba自旋劈裂. 本文研究了Al_0.6Ga_0.4N/GaN/Al_0.3Ga_0.7N/Al_0.6Ga_0.4N量子阱中第一子带的Rashba 系数和Rashba自旋劈裂随Al_0.3Ga_0.7N插入层(右阱)的厚度w_s以及外加电场的变化关系, 其中GaN层(左阱)的厚度为40-w_s Å. 发现随着w_s的增加, 第一子带的Rashba系数和Rashba自旋劈裂首先增加, 然后在w_s>20 Å 时它们迅速减小, 但是w_s>30 Å时Rashba自旋劈裂减小得更快, 因为此时k_f也迅速减小. 阱层对Rashba系数的贡献最大, 界面的贡献次之且随w_s变化不是太明显, 垒层的贡献相对比较小. 然后, 我们假w_s=20 Å, 发现外加电场可以很大程度上调制该体系的Rashba系数和Rashba自旋劈裂, 当外加电场的方向同极化电场方向相同(相反)时, 它们随着外加电场的增加而增加(减小). 当外加电场从-1.5×10⁸ V·m^-1到1.5×10⁸ V· m^-1变化时, Rashba系数随着外加电场的改变而近似线性变化, Rashba自旋劈裂先增加得很快, 然后近似线性增加, 最后缓慢增加. 研究结果表明可以通过改变GaN层和Al_0.3Ga_0.7N层的相对厚度以及外加电场来调节Al_0.6Ga_0.4N/GaN/Al_0.3Ga_0.7N/Al_0.6Ga_0.4N量子阱中的Rashba 系数和Rashba自旋劈裂, 这对于设计自旋电子学器件有些启示.     

Valence-band structure and optical absorption inp-type GaAs–Al0.3Ga0.7As multi-quantum-well infrared photodetectors under an electric field

Hole structure of a GaAs–Al_0.3Ga_0.7Asp-type multiple quantum well (MQW) subjected to an electric field parallel to the growth axis is studied using the envelope-function approximation and taking into account the valence subband mixing. The system considered in this work consists of five GaAs wells and six thick Al_0.3Ga_0.7As barriers. The valence subband structure and the optical-absorption coefficient are calculated as functions of the electric-field strength for various doping levels. The subband structure is shown to be nonparabolic and anisotropic in the plane of the layers with a four-fold symmetry. The spin splitting due to the lack of specular symmetry of quantum wells is a growing function of the electric-field strength. The calculated optical absorption is in good agreement with the experimental spectra.     

Intersubband spin-orbit coupling and spin splitting in symmetric quantum wells

In semiconductors with inversion asymmetry, spin-orbit coupling gives rise to the well-known Dresselhaus and Rashba effects. If one considers quantum wells with two or more conduction subbands, an additional, intersubband-induced spin-orbit term appears whose strength is comparable to the Rashba coupling, and which remains finite for symmetric structures. We show that the conduction band spin splitting due to this intersubband spin-orbit coupling term is negligible for typical III-V quantum wells.     

Linear and Nonlinear Intersubband Optical Absorptions and Refractive Index Changes in InGaN Strained Single Quantum Wells： Strong Built-in Electric Field Effects

Considering the strong built-in electric field （BEF） effects due to the spontaneous and piezoelectric polarizations, the intersubband optical absorptions and refractive index changes for an InxGa1-xN/AlyGa1-yN strained single quantum well are studied theoretically within the framework of the density matrix method and effective-mass approximation. The linear, third-order nonlinear and total absorption coefficients and refractive index changes are calculated as a function of the incident optical intensity and photon energy. Our results show that both the incident optical intensity and the strong BEF have great influence on the total absorptions and refractive index cllanges. The results are significant for designing some important photodetectors and the photonic crystal devices with adjustable photonic band structures.     

Interface contributions to the spin-orbit interaction parameters of electrons at the (001) GaAs/AlGaAs interface

One-body mechanisms of spin splitting of the energy spectrum of 2D electrons in a one-side doped (001) GaAs/Al _x Ga_{1 ? x} As quantum well have been studied theoretically and experimentally. The interfacial spin splitting has been shown to compensate (enhance) considerably the contribution of the bulk Dresselhaus (Bychkov-Rashba) mechanism. The theoretical approach is based on the solution of the effective mass equation in a quasi-triangular well supplemented by a new boundary condition at a high and atomically sharp hetero-barrier. The model takes into account the spin-orbit interaction of electrons with both bulk and interfacial crystal potential having C _2v symmetry, as well as the lack of inversion symmetry and nonparabolicity of the conduction band in GaAs. The effective 2D spin Hamiltonian including both bulk and interface contributions to the Dresselhaus (α_BIA) and Rashba (α_SIA) constants has been derived. The analytical relation between these constants and the components of the anisotropic nonlinear g-factor tensor in an oblique quantizing magnetic field has been found. The experimental approach is based, on one hand, on the detection of electron spin resonance in the microwave range and, on the other hand, on photoluminescence measurements of the nonparabolicity parameter. The interface contributions to α_BIA and α_SIA have been found from comparison with the theory.     

Influence of exciton energy on intersubband transition of chirped superlattice GaAs/AlGaAs quantum cascade laser

The influence of exciton energy on intersubband transition was simulated for a chirped supperlattice quantum cascade laser of GaAs/Al_xGa_1-xAs. Exciton energy was modelled as a function of QW width for alloys of various percentages of constituent elements. The results showed that the exciton energy decreased proportionally with increasing QW width. Models were also generated to study exciton energy as a function of the percent alloy contents of Al_xGa_1-xAs barriers for QWs of various widths. Exciton energy showed characteristics of higher discrete energy when QW width was narrower. Transition energy was also simulated from e₁ and e₂ to the 1s exciton state as functions of applied electric field at various QW widths. Our simulation results showed that the transition energy from e₂ to the 1s exciton state increased proportionally to the increasing strength of the electric field. This transition energy was indicative of THz range radiation.     

Electron spin resonance and Rashba field in GaN-based materials

We discuss problem of Rashba field in bulk GaN and in GaN/Al_xGa_1−xN two-dimensional electron gas, basing on results of X-band microwave resonance experiments. We point at large difference in spin-orbit coupling between bulk material and heterostructures. We observe coupled plasmon-cyclotron resonance from the two-dimensional electron gas, but no spin resonance, being consistent with large zero-field spin splitting due to the Rashba field reported in the literature. In contrast, small anisotropy of g-factor of GaN effective mass donors indicates rather weak Rashba spin-orbit coupling in bulk material, not exceed 400 G, α_BIA<4×10⁻¹³ eVcm. Furthermore, we observe new kind of electron spin resonance in GaN, which we attribute to surface electron accumulation layer. We conclude that the sizable Rashba field in GaN/Al_xGa_1−xN heterostructures originates from properties of the interface.     

Symmetry and spin dephasing in (110)-grown quantum wells

Symmetry and spin dephasing in (110)-grown GaAs quantum wells (QWs) are investigated applying magnetic field induced photogalvanic effect and time-resolved Kerr rotation. We show that magnetic field induced photogalvanic effect provides a tool to probe the symmetry of (110)-grown quantum wells. The photocurrent is only observed for asymmetric structures but vanishes for symmetric QWs. Applying Kerr rotation we prove that in the latter case the spin relaxation time is maximal; therefore, these structures set the upper limit of spin dephasing in GaAs QWs. We also demonstrate that structure inversion asymmetry can be controllably tuned to zero by variation of delta-doping layer positions.     

Properties of AlyGa1-yN/AlxGa1-xN/AlN/GaN Double-Barrier High Electron Mobility Transistor Structure

Electrical properties of Al_yGa_1-yN/Al_xGa_1-xN/AlN/GaN structure are investigated by solving coupled Schrödinger and Poisson equation self-consistently. Our calculations show that the two-dimensional electron gas (2DEG) density will decrease with the thickness of the second barrier (Al_yGa_1-yN) once the AlN content of the second barrier is smaller than a critical value y_c, and will increase with the thickness of the second barrier (Al_yGa_1-yN) when the critical AlN content of the second barrier y_c is exceeded. Our calculations also show that the critical AlN content of the second barrier y_c will increase with the AlN content and the thickness of the first barrier layer (Al_xGa_1-xN).     

Built-in electric field effect on the linear and nonlinear intersubband optical absorptions in InGaN strained single quantum wells

Considering the strong built-in electric field (BEF) induced by the spontaneous and piezoelectric polarizations and the intrasubband relaxation, we investigate the linear and nonlinear intersubband optical absorptions in In_xGa_1-xN/Al_yGa_1-yN strained single quantum wells (QWs) by means of the density matrix formalism. Our numerical results show that the strong BEF is on the order of MV/cm, which can be modulated effectively by the In composition in the QW. This electric field greatly increases the electron energy difference between the ground and the first excited states. The electron wave functions are also significantly localized in the QW due to the BEF. The intersubband optical absorption peak sensitively depends on the compositions of In in the well layer and Al in the barrier layers. The intersubband absorption coefficient can be remarkably modified by the electron concentration and the incident optical intensity. The group-III nitride semiconductor QWs are suitable candidate for infrared photodetectors and near-infrared laser amplifiers.     

Magnetoelectric Cr<Subscript>2</Subscript>O<Subscript>3</Subscript> and relativity theory

Based on the dielectric continuum phonon model, uniaxialmodel and force balance equation the mobility of two dimensional electrongas in wurtzite Al_xGa_1-xN/GaN/Al_xGa_1-xN quantum wells isdiscussed theoretically within the temperature range dominated by opticalphonons. The dependences of the electron mobility on temperature, Al molarfraction and electron sheet density are presented including hydrostaticpressure effect. The built-in electric field is also taken into account. Itis found that under normal pressure the main contribution to the mobility isfrom the scattering of interface optical phonons in narrow (for well widthd < 12 Å) and wide (for d > 117 Å and d > 65 Å for finitelythick barriers and infinitely thick ones, respectively) wells, whereas thatis from the scattering of confined optical phonons in a well with anintermediate width. It is shown that the electron mobility decreases withincreasing Al molar fraction and temperature, whereas increases obviouslywith increasing electron sheet density. The theoretical calculated electronmobility is 978 cm²/V?s which is higher than an available experimentaldata 875 cm²/V?s when x equals to 0.58 at room temperature. Theresults under hydrostatic pressure considering the modification of strainindicate that the mobility increases slightly as hydrostatic pressureincreases from 0 to 10 GPa.     

Effect of well thickness on the Rashba spin splitting and intersubband spin-orbit coupling in AlGaN/GaN/AlGaN quantum wells with two subbands

By projecting the characteristic equation into the subspace of the conduction band, the Rashba spin splitting coefficient for the first two subbands (α₁, α₂) and the intersubband spin-orbit coupling coefficient (η₁₂) in AlGaN/GaN quantum well structure are obtained. Then sizable α₁, α₂ and η₁₂ in QWs are calculated by solving the Schrödinger and Poisson equations self-consistently. We find that the internal electric field is crucial for considerable spin-orbit coupling effect in III-nitride QWs and the spin-orbit coupling coefficient can be greatly modulated by the well thickness. Compared with the Rashba coefficient, the intersubband spin-orbit coupling coefficient is basically of the same order of magnitude. The results show the great possibility of spin manipulation in low-dimensional semiconductors, and III-nitride QWs are candidates for the design of spintronic devices.